200404266 玖、發明說明： 【發明所屬之技術領域】 本毛明一般與由電細控制在光柵顯示器中顯示影像之方 法有關。特定言之，本發明係關於用於重構、縮放、離散 的儲存影像或對其實施透視投影（其目的係在光柵顯示器上 呈現較高品質之元素）所必需之各向異性過濾機構。上述之 離散儲存影像下文將稱為紋理。特定言之，本發明係關於 在一提供具有一解析度之紋理元素的一圖形系統中，根據 一軌跡所接觸之指定數量之紋理元素分析與修正該軌跡之 方法。 【先前技術】 「軌跡」係一物體之圖像元素（像素）在曲面上的透視投 影。「執跡」可為將一物體之正方形圖像元素（像素）於一規 則texel格柵（texture-element grid;紋理元素格柵）上之透視 投影之近似結果重製到一曲面上之凸四邊形呈現。 在與物體之圖像元素（像素）有關的紋理中，已知的圖形系 統如OpenGL圖形系統以此一方式操作，使物體之一像素之 軌跡具有一或多個具有與其有關之所需解析度之紋理元 素，軌跡近似為正方形。缺點係，此處的近似總是受一或 太大或太小之正方形影響且沒有考慮軌跡的形狀。 所舄要之解析度在軌跡下導致texel格柵中之kxei尺寸。 對於預定之texel尺寸存在各種的mipmap位準。若所選解析 度導致不具有一適合解析度（位準）imipm邛之“Μ〗尺寸， 則必須以較高代價計算該紋理。 88012 -6- 200404266 從此先前技術開始，本 跡之改進方法。 * 的係提供一用於修正軌 專利範園第β之方法達到此目的。200404266 (1) Description of the invention: [Technical field to which the invention belongs] This Maoming is generally related to the method of displaying images on a raster display by electronic fine control. In particular, the present invention relates to an anisotropic filtering mechanism necessary for reconstructing, zooming, and discretely storing images or performing perspective projection on them (the purpose of which is to present higher-quality elements on a raster display). The above-mentioned discretely stored images will be referred to as textures hereinafter. In particular, the present invention relates to a method of analyzing and correcting a trajectory based on a specified number of texels that a trajectory touches in a graphics system that provides a texture element with a resolution. [Prior art] "Track" is the perspective projection of an image element (pixel) of an object on a curved surface. "Tracking" can be an approximation of the perspective projection of a square image element (pixel) of an object onto a regular texel grid (texture-element grid) to a convex quadrilateral on a curved surface Render. In textures related to the image elements (pixels) of an object, known graphics systems, such as the OpenGL graphics system, operate in such a way that the trajectory of one pixel of an object has one or more of the required resolutions associated with it Texture element, the track is approximately square. The disadvantage is that the approximation here is always affected by a square that is too large or too small and does not consider the shape of the trajectory. The required resolution leads to the kxei size in the texel grid under the trajectory. There are various mipmap levels for the predetermined texel size. If the selected resolution does not have a "M" size suitable for the resolution (level) imipm 邛, then the texture must be calculated at a higher cost. 88012 -6- 200404266 Starting from this prior technique, this trace is an improved method. * Means to provide a method for amending the patent paradigm β to achieve this goal.
【發明内容】 J 本發明提供一種方法，用於在 理元素的_圖形系，統巾 、〜、有—解析度之纹 紋理元素分析與修正該軌跡，其包括：疋數κ U)決定軌跡的尺度或形狀，· (b)基於該指定數量之纟 尺度或形狀，指定盘、：步驟(a)中所決定的 度;及 …軌称有關的紋理元素的解析 ⑷決定圖形系統是否提供具 度之紋理元素， ）中所扣疋《解析 (C·1)若圖形系統提供具有步驟(b)中所指定之解析度 之紋理元素，保持該軌跡；及 ㈣若圖形系統未提供具有步驟(b)中所指定之 度〈紋理元素，則選擇由該圖形系統提供且 -個別解析度之紋理元素，且減小該軌跡：尺 寸，從而由具有該減小尺寸之該軌跡所接觸之纹 心素之數量係本質上等於或小於該指定數量。 錢“技術進行—亦可稱料各向 盥it卜丁 Π，*代η 、“又過濾， 不同本發明說明以—最佳方式向軌跡分配許多且有 指定解析度且因而具有指定尺寸之 /、有 丄、 里兀素，而非藉 -%全包圍該軌跡或完全包含在該軌跡中之正方形對該 88012 200404266 軌跡的「粗略」近似。 _ 若&要，# p 起精由紋理元素重疊該軌跡， ^要依據本發明對軌跡進行 跡最佳分配紋理元素。 υ 以搜仔向勒 依據一較佳具骨曹音# γ丨 解析度之'-元明::用::有㈣各種 騍（c.2)中所選擇之指定 有在乂 ^ FI ^ ^ ν ^ 又向下《一解析度。較佳地， 邊圖开y系統以各種mi 之紋理元素。 以…式提供具有各種解析度 依據一較佳具體實施例， 、 中浐宕勺門、、紕 、、、了决疋摄解析度，在步驟（b) 才曰疋匕圍琢軌跡之矩形， 邊 同點係位於孩矩形的 =理T 矩形，不存在具有相關尺寸即解析 用於達職要的數量p，則在上述具體實施 ::開:*中指定根據圖形系統可利用之解析度且根據 葬：兀素〈數量所定義之一夾緊框或央緊正方形。隨後， 二由將軌跡之最高點偏移至夾緊框的邊緣減小軌跡之尺 ，佳地、，基於軌跡之參數厚度或膨服指定上述矩形及爽 ，、框，厚度參數重製軌跡的一縱向變形。 依據另-較佳具體實施例，決定該軌跡之尺度或形式的 :時:進行一關於軌跡邊緣是否超出指定尺度之決定，且 右為是，則此時減少軌跡的尺寸直到邊緣的尺度小於 於指定尺度。 … Q此，本發明方法提供依據一項具體實施例亦可由使用 杈制以用於分析與修正一軌跡之新穎方法。 88012 -8- 200404266 為了擴取離散紋理影傻，以、强二士 〜像必須碩入且由處理單元處理規 則texel格柵之所有正方形元素加义由軌跡區域重疊。本 發明方法允許限制軌跡所接觸之_的數量及軌跡之邊緣 的長度。依據本發明’為此目的提供—額外的控制輸入信 號、’精確言之’即性能參數P。可由使用者提供此參數p。 由定義最大邊緣長度之另—參數定軌跡邊緣長度之限 制。例如，可對此參數Emax進行硬編碼。 本發明的優點係，藉由設定控制輸入信號p，可達成一方 面為擴取/重構影像品質（採用大數量的㈣），$ —方面為 處理速度（採則、數量的texel)之間的折衷。限制邊界邊緣 的好處係，可大大降低用於隨後程序中進一步處理軌跡所 需要的硬體費用。此等隨後程序包括如決定由軌跡重疊的 texel及/或加權此等指stexel。藉由夾緊邊緣長度，可明顯 減少與此等處理步驟有關之硬體費用。 通常，可向每一 teXel定位之光柵程序提供本發明方法得 出的資料。 依據本發明之一較佳具體實施例，如上所述，向與軌跡 有關的一紋理提供具有各種解析度之複數個所謂的影像映 圖，該等影像映圖亦可稱作mipmap。為了指定解析度，根 據軌跡之尺度或形狀且根據所要呈現之軌跡之需要影像品 質，決定在一 teXel格柵中由軌跡所接觸之“^丨之尺寸。根 據已如此決定之texel尺寸，確定在複數個影像映圖中是否 存在有關的texel尺寸與已確定之texel尺寸匹配之一影像映 圖。若是，採用個別影像映圖來呈現該軌跡。然而若沒有 88012 200404266 此類個別影像映圖，如上所述減 丨心鹌y執鄱 < 尺寸，因而據 軌跡的影像品質，為呈現該軌 ， &擇具有沿者需要解析度 向下《解析^且具有個別texeI尺寸之一可用影像映圖。_ 較佳地二精由本質上標示_texeI格柵中由軌跡所接觸之— texels數f的性能參數c指定影像品質。 依據上述較佳具體實施例， 口租# 、 卸況明本質上兩種限制用於 主現軌跡<texel之數量（根據性能參❹的 技術。若具有較低解析度之紋理影 ）万法及/戍 • 〜像 < 預過濾型式-所謂的 mipmap-係可用的，則在戽 • 予度貝成的基礎上計算一適當的 mlpmaP位準。因此，接著以一 、 心口万式決疋texel格柵中正 万形texel的尺寸。此位準钭营 冲才係基々軌跡的實際空間尺度 J ’·。若沒有可利用的具有所需要位準之預過滤影像 =(mipnrp)，以一選擇方式藉由收縮軌跡之邊界（邊緣）減 ’跡之區域。根據下一可用I , 〜像陕圖（mlpmap)之形狀、 性月匕參數p及texei尺寸收輪軎 邊緣及/或减少區域，在最不有[Summary of the Invention] J The present invention provides a method for analyzing and correcting the trajectory of the _ graphic system of the element, the pattern, the texture element with the resolution, and the trajectory, including: the number 疋 U) to determine the trajectory (B) Specify the disk based on the specified number of dimensions or shapes: the degree determined in step (a); and ... analysis of the texture elements related to the track name, determine whether the graphics system provides The texture elements in degrees) are deducted in "Analysis (C · 1) if the graphics system provides a texture element with the resolution specified in step (b), and the trajectory is maintained; and if the graphics system does not provide a step ( The degree specified in b) <texture element, then select the texture element provided by the graphics system with an individual resolution, and reduce the trajectory: size, so that the center of the texture touched by the trajectory with the reduced size The number of primes is essentially equal to or less than the specified number. "Technical progress-you can also weigh the material in each direction, it can be weighed, and it is filtered, different. The present invention describes in an optimal way to assign a large number of trajectories with a specified resolution and therefore a specified size / , 丄, and Li Wusu, instead of the "rough" approximation of the 88012 200404266 trajectory, the square that completely surrounds the trajectory or completely contains the trajectory by-%. _ If & want, # p from the texture element to overlap the track, ^ the best allocation of texture elements to the track in accordance with the present invention. υ Yisou Xiangle based on a better with a bone Cao Yin # γ 丨 The resolution of '-Yuanming :: use :: 有 ㈣ various kinds of 骒 (c.2) The choice specified in 乂 ^ FI ^ ^ ν ^ again down to a resolution. Preferably, the edge graph system is composed of various mi texture elements. A preferred embodiment with various resolutions is provided in the form of:,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, and the trajectories of the trajectory in step (b), The edge point is located in the rectangular rectangle of the child rectangle. If there is no relevant size, that is, the number p used to fulfill the job requirements, then the above specific implementation :: On: * is specified according to the resolution available in the graphics system and According to the funeral: one of the clamping frames or central squares as defined by the quantity. Subsequently, the offset of the trajectory is reduced by shifting the highest point of the trajectory to the edge of the clamping frame. Ideally, the above-mentioned rectangle and frame are specified based on the parameter thickness or expansion of the trajectory. A longitudinal deformation. According to another preferred embodiment, the scale or form of the trajectory is determined by: Hour: a decision is made as to whether the edge of the trajectory exceeds the specified scale, and the right is yes, then the size of the trajectory is reduced until the edge is smaller than Specify the scale. … Q. Therefore, the method of the present invention provides a novel method that can also be used to analyze and modify a trajectory according to a specific embodiment. 88012 -8- 200404266 In order to expand the discrete texture shadow, the image must be large and all the square elements of the texel grid must be superimposed by the processing unit to overlap the trajectory area. The method of the present invention allows to limit the number of _ contacted by the trajectory and the length of the edges of the trajectory. Provided for this purpose according to the present invention-an additional control input signal, "exactly" the performance parameter P. This parameter p can be provided by the user. The limit of the edge length of the track is determined by another parameter that defines the maximum edge length. For example, this parameter Emax can be hard-coded. The advantage of the present invention is that, by setting the control input signal p, it can be achieved on the one hand to acquire / reconstruct the image quality (using a large number of ㈣), and on the other hand, it is between the processing speed (selection, number of texel). Eclectic. The benefit of limiting the edge of the boundary is that it can greatly reduce the hardware cost required for further processing of the trajectory in subsequent programs. These subsequent procedures include, for example, texel overlapping by trajectories and / or weighting these texels. By clamping the edge length, the hardware costs associated with these processing steps can be significantly reduced. In general, the raster program for each teXel positioning can be provided with the information obtained by the method of the present invention. According to a preferred embodiment of the present invention, as described above, a texture related to a trajectory is provided with a plurality of so-called image maps having various resolutions, and these image maps may also be referred to as mipmaps. In order to specify the resolution, according to the size or shape of the trajectory and the required image quality of the trajectory to be rendered, the size of "^ 丨" touched by the trajectory in a teXel grid is determined. According to the texel size that has been determined in this way, Is there an image map in which the relevant texel size matches the determined texel size in the multiple image maps. If so, the individual image maps are used to present the trajectory. However, if there is no such image map of 88012 200404266 as above According to the image quality of the track, according to the image quality of the trajectory, in order to present the track, & select one that has the resolution required by the follower and parse ^ and has one of the available texeI sizes. _ It is better to specify the image quality by the performance parameter c of the texels number f in the texeI grid, which is essentially labeled _texeI. According to the above-mentioned preferred embodiment, 口 租 #, unloading state is essentially Two kinds of restrictions are applied to the number of main trajectories < texel (based on performance reference techniques. For textures with lower resolution) Wanfa and / 戍 • ~ Image < The filtering type-the so-called mipmap-is available, then an appropriate mlpmaP level is calculated on the basis of 度 degrees. Therefore, the size of the regular texel in the texel grid is determined by the following methods: This level is the actual spatial dimension of the base trajectory J '·. If no pre-filtered image with the required level is available = (mipnrp), the boundary of the trajectory is contracted in a selective manner ( Edge) minus the area of the trace. According to the next available I, ~ the shape like the mlpmap (mlpmap), the sex month parameter p and the texei size to close the edge and / or reduce the area, in the least
、月/兄下，下一可用影像映圖本身係最$ & A % 口+郯你取初的基礎映圖。 衣據本發明的另一較佳且两曲舍、Α 、 季乂佳具骨豆貫施例’最先分析由其四個 绫”入四邊形軌跡之有關的區域及/或形狀及/或邊 、乏二間％脹。此分析包括以下步驟： -決定可為順時針或為逆時針之軌跡的旋轉方向. -計算-說明軌跡縱向變形之程度之各向異性厚度參數； •決足軌跡之邊界框； ’ Λ々万式產生夾緊最初軌跡之線性收縮型式之夾緊框， 使得（（收縮軌跡）之任何邊緣之水平寬度及垂直高度不超 88012 -10- 200404266 過預定義限制）。基於上述邊緣Emax之最大長度值指定此 預定義限制。此外，夾緊框的尺度取決於厚度參數且如 此設定以至央緊框重疊的t e X e丨數量不超過性能參數p所_ -指定的邊界。 . 一旦以上述方式分析引入之軌跡，隨後評估如此獲得且 已分析的資訊，從而產生代表可能已修正之軌跡以及相關 mipmap位準及相關放大位準之輸出資料。此處主要涉及將 取初軌跡之所有頂點之最初座標向由所計算之mipmap位準 指足之座標系統轉換。若必要，將軌跡之所有頂點投影於 夾緊框上將引起軌跡的額外收縮。 因而，本發明的優點係，如下修正引入之軌跡座標 -邊緣九度或邊緣咼度最好不超過已進行硬編碼之最大長 度 Emax， 軌跡所重疊之texei的數量等於或小於使用者所預定義之 此等texel的數量， -若根據一大於〇的mipmap位準選擇縮小比例，則保存軌 跡形狀，及 -避免所擷取影像的空間及時間不連續。 依據本發明之一較佳具體實施例，在一硬體管線之形狀 《硬體方面實施本發明方法，其致動加速處理複數個軌跡。 【實施方式】 參考圖1，下面將概述依據一較佳具體實施例之本發明方 法’圖1所示個別處理步騾將參考剩餘圖式詳細說明。 本發明方法從接收說明該軌跡之資料之區塊1 〇 〇開始。在 88012 -11- 200404266 下面說明中經常採用術語「軌跡」，其係凸四邊形結構且代 表一正方形圖像元素向曲面之透視投影之近似結果。 圖！所示之流程圖中，矩形代示下面將詳細說明之主要處^ 理步驟。在圖1之平行四邊形中採用圖示法所顯示之資料結_· 構中鍺存處理步驟的結果。採用此等結果作為下一處理階 段的輸入信號。下面將詳細說明個別處理步騾，已選擇一 數學向量符號（以黑體表示）用於簡化該說明。 一旦在區塊1〇〇中接收到說明軌跡之資料，在區塊1〇2中 可用說明軌跡之頂點之向量Vi’其中㈣，u 2, 3(說明該較 佳具m貝施例係基於假定軌跡為一四邊形）。 在隨後之區塊104中，採用區塊1〇2中所提供之軌跡資訊 進行軌跡分析。一方面，此軌跡分析導致確定一軌跡旋轉 方向d，其如供於區塊丨〇6中且提供於區塊丨〇8中之輸出。此 外，區塊1 04中之軌跡分析產生提供於區塊丨丨〇中之厚度參 數t。基於提供於區塊11〇中之厚度參數t，且基於提供於區 塊112中一外部性能參數p，計算提供於區塊ιΐ6中之夾緊尺 寸^。性能參數p指定軌跡所接觸及/或重疊之化“丨的數量。 在區塊120中計算所需要的mipmap位準。一方面，作為外 部參數，區塊120中之計算接收來自區塊122之最大mipmap 位卞Mmax之一標示。此外且在區塊1〇2所提供之軌跡資料的 基礎上，在區塊U4中計算一邊界框，其尺度b_、b_提供 毛區塊126中且#疋供於區塊120中用於計算mipmap位準。區 塊12〇中所計算的miPmap位準m接著提供於區塊128中且輸 出於區塊13 0中。 88012 -12- 200404266 在區塊11 6中所提供之夾緊尺寸c〇及區塊中所提供之 ―啊位準_基礎上，在區塊⑴中進行mipmap校正（參 N 及圖1B)。mipmaP校正導致提供於區塊134中已修 正之夾緊尺寸Cm。向區塊136提供已修正夾緊尺寸其中 、、、“ Θ軌跡’ <吏其週合夾緊尺寸^所定義的夾緊矩形。區 塊S 136中所進仃〈計算_方面導致將提供於區塊⑴及 中之修正後的軌跡資料V'及縮放因數fx、fy。如亦可在圖lb 中之所見，處理級136除接收修正後的夾緊尺寸、以外，還 接收區塊102中所提供之軌跡資料（參見項目B)及區塊124中 所计异《有關邊界框bmu、之資料（參見項目q。 向區塊142提供區塊138中所提供之修正後的軌跡資料^ 及mipmap位率m，其中在區塊132所接收之資料及資訊的基 石疋上，向一延取11111)111邛位準進行變換，從而變換/轉換後的 軌跡貝料V%提供於區塊144中，該資料將在區塊146中輸出。 此外，在提供於區塊14〇中之縮放因數&、乙的基礎上， 在區塊148中減小厚度，區塊148接收提供於區塊ιι〇中的厚 度參數（參見項目D)及來自區塊丨4〇的輸入。此外，區塊丨48 從區塊150接收一減小厚度1的適當演算法。修正後的厚度 參數t’接著在區塊152中輸出。在區塊154中所提供之放大參 數及區塊丨52中所提供之修正後的厚度參數1，的基礎上，在 區塊156中計算擴大偏移或放大偏移，從而一放大位準^，提 供於區塊158中。在區塊160中所提供之演算法的基礎上且 在區塊158所提供之擴大步驟的基礎上，及在mipmap位準m 的基％:上在區塊162中向所選取mipmap位準進行變換，從 88012 •13- 200404266 而在區段164中產生一修正後的擴大步驟Γ*，其亦在區塊i46 中輸出。 下面將詳細說明圖1之個別區 圖2 _示配置於橫跨x軸及y軸之一紋理空間中之凸軌跡 200之範例。此紋理空間亦具有配置於其中由複數個正方形 texel元素組成之texei格栅（軌跡重疊其中—些）。圖2顯示頂 點向量vG至vs及邊緣向量、至^。在本發明方法中，頂點向 量vG至v3作為輸入資料提供。 用於指定一適當詳細位準以代表該軌跡之重要參數係所 謂的軌跡「厚度」t。圖3詳細顯示一四邊形軌跡之此厚度 參數。圖3中，顯示四個頂點向量v#v3及分別接合相對= 點ν0與ν2’及'與％的兩個高度向量ho#。此外，圖3說明 兩個厚度參數0tl，由所顯示之兩個厚度參數t。與〖之 者決定最終的厚度參數丨。 1 小 如所見，厚度參數t〇定義延伸穿過頂點Μ%且此外係血 南度向量h°平行之兩直線之間的距離。同樣，厚度向量β 示延伸穿過頂點V#V2且係與高度向量\切之兩 ^ 的距離。 < ^ 在圖3所示參數的基礎上 參數t。 依據下面的計算說明計算厚度 88012 -14- 200404266 ^ _ ί ^ $0¾ h. = 〇 \F/hj 否則 ’ = 0 如果A。4=0 l^/maxG。，、） 否則 ㈣本發@之—較佳具时 索引之旋轉太Α Η 1 士 Τ 了視而要計算頂點 疋柊万向d，可在隨後計算指 轉方向。此从 、、，彖屬性中採用該旋 說明計算旋轉方向d及面積A: ㈣下面的計异 d=sign(hz) A=F/2 其中： 橫跨hG與\之平行四邊形之面積。 方向d具有順時針旋轉之數值+1及逆時針旋轉之數值心 在的情況下’軌跡退化成點或線，且在此情況 下，旋轉方向d係0。 決定厚度參數t後，且視需要決定旋轉方向d及面積a後， 接著計算夾緊尺寸c。夾緊尺寸0係橫跨厚度參數1之進程之 線性函數，該進程係定位於可設定之性能參數p與表Next, next month / brother, the next available image map itself is the most basic image. According to another preferred embodiment of the present invention, the two qusha, A, and ji ji jia jia dou dou examples "first analyze the relevant areas and / or shapes and / or edges of the four trajectories" into the quadrilateral trajectory. The lack of two swells. This analysis includes the following steps:-Determine the direction of rotation of the trajectory that can be clockwise or counterclockwise.-Calculate-Anisotropic thickness parameters that describe the degree of longitudinal deformation of the trajectory; Bounding box; 'Λ々wan type produces a clamping frame of the linear contraction type that clamps the original trajectory, so that (the horizontal width and vertical height of any edge of the (contraction trajectory) does not exceed 88012 -10- 200404266 over a predefined limit). Specify this predefined limit based on the maximum length value of the above edge Emax. In addition, the dimensions of the clamping frame depend on the thickness parameter and are set so that the number of te X e 丨 that the central tight frame overlaps does not exceed the boundary specified by the performance parameter p- ... Once the introduced trajectories are analyzed in the manner described above, the information thus obtained and analyzed is subsequently evaluated to produce inputs representing the trajectories that may have been modified, as well as the relevant mipmap levels and the relevant magnification levels. The information here mainly involves the conversion of the initial coordinates of all vertices of the initial trajectory to the coordinate system calculated by the calculated mipmap level. If necessary, projecting all vertices of the trajectory on the clamping frame will cause the trajectory Therefore, the advantage of the present invention is that the following introduced trajectory coordinates-edge nine degrees or edge 咼 degrees should preferably not exceed the maximum length Emax which has been hard-coded, and the number of texei on which the tracks overlap is equal to or less than the user The predefined number of these texels,-if the reduction ratio is selected according to a mipmap level greater than 0, the shape of the trajectory is saved, and-the spatial and temporal discontinuity of the captured image is avoided. In the embodiment, the shape of a hardware pipeline "implements the method of the present invention in terms of hardware, actuates accelerated processing of a plurality of trajectories. [Embodiment] Referring to Fig. 1, the method of the present invention according to a preferred embodiment will be outlined below 'The individual processing steps shown in Figure 1 will be described in detail with reference to the remaining drawings. The method of the present invention receives block 1 from which information describing the trajectory is received. Start. In the following description of 88012 -11- 200404266, the term “track” is often used, which is a convex quadrilateral structure and represents the approximate result of the perspective projection of a square image element onto a curved surface. Figure! In the flowchart shown, the rectangles represent the main processing steps which will be described in detail below. The results of the germanium deposit processing steps in the structure of the data structure shown in the parallelogram in Figure 1 using the graphic method are shown. These results are used as input signals for the next processing stage. The individual processing steps will be described in detail below. A mathematical vector symbol (indicated in bold) has been selected to simplify the description. Once the information describing the trajectory is received in block 100, the vector Vi 'describing the vertices of the trajectory can be used in block 102, where ㈣, u 2, 3 (indicating that the preferred embodiment is based on (Assuming the trajectory is a quadrilateral). In subsequent block 104, the trajectory information provided in block 102 is used for trajectory analysis. On the one hand, this trajectory analysis results in determining a trajectory rotation direction d, such as the output provided in block 丨 06 and provided in block 丨 08. In addition, the trajectory analysis in block 104 generates the thickness parameter t provided in block 丨 丨 〇. Based on the thickness parameter t provided in block 11 and the external performance parameter p provided in block 112, the clamping dimensions provided in block ι6 are calculated ^. The performance parameter p specifies the number of contacts and / or overlaps of the trajectory "丨. The required mipmap level is calculated in block 120. On the one hand, as an external parameter, the calculation in block 120 receives the data from block 122. The maximum mipmap is indicated by one of 卞 Mmax. In addition, based on the trajectory data provided in block 102, a bounding box is calculated in block U4, and its dimensions b_, b_ are provided in the gross block 126 and #疋 It is used in block 120 to calculate the mipmap level. The miPmap level m calculated in block 120 is then provided in block 128 and output in block 130. 88012 -12- 200404266 in block 11 Based on the clamping size c0 provided in 6 and the ah level provided in the block, a mipmap correction is performed in block ⑴ (see N and Figure 1B). The mipmaP correction results in a block 134 The revised clamping dimension Cm is provided in block 136. The corrected clamping dimensions are provided to the block 136, among which, ", Θ locus" < the clamping rectangle defined by its surrounding clamping dimensions ^. The "calculation_" aspects performed in block S 136 result in the modified trajectory data V 'and the scaling factors fx, fy to be provided in blocks ⑴ and. As can also be seen in Figure lb, in addition to receiving the corrected clamping dimensions, the processing stage 136 also receives the trajectory data provided in block 102 (see item B) and the differences in block 124 Information about the bounding box bmu, (see item q. Provide the modified trajectory data ^ provided in block 138 and the mipmap bit rate m to block 142, which is on the cornerstone of the data and information received in block 132. , To take a 11111) 111 邛 level to transform, so that the transformed / converted trajectory shell material V% is provided in block 144, and this data will be output in block 146. In addition, on the basis of the scaling factors & B provided in block 140, the thickness is reduced in block 148, and block 148 receives the thickness parameters provided in block ιο (see item D) and Input from block 丨 40. In addition, block 48 receives an appropriate algorithm for reducing thickness 1 from block 150. The modified thickness parameter t 'is then output in block 152. Based on the enlargement parameters provided in block 154 and the corrected thickness parameter 1 provided in block 丨 52, the enlargement offset or enlargement offset is calculated in block 156, thereby an enlargement level ^ , Provided in block 158. Based on the algorithm provided in block 160 and the expansion steps provided in block 158, and at the base% of the mipmap level m: on block 162 to the selected mipmap level The transformation, from 88012 • 13- 200404266, produces a modified expansion step Γ * in section 164, which is also output in block i46. The individual regions of FIG. 1 will be described in detail below. FIG. 2 _ shows an example of a convex trajectory 200 arranged in a texture space spanning one of the x-axis and the y-axis. This texture space also has a texei grid (trajectories overlapping some of them) composed of a plurality of square texel elements. Figure 2 shows vertex vectors vG to vs and edge vectors, to ^. In the method of the present invention, vertex vectors vG to v3 are provided as input data. An important parameter for specifying an appropriate level of detail to represent the trajectory is the so-called trajectory "thickness" t. Figure 3 shows this thickness parameter of a quadrilateral track in detail. In FIG. 3, four vertex vectors v # v3 and two height vectors ho #, which are respectively connected to the opposite points ν0 and ν2 'and' and%, are shown. In addition, FIG. 3 illustrates two thickness parameters 0tl, from which two thickness parameters t are displayed. Whichever determines the final thickness parameter. 1 small As can be seen, the thickness parameter t0 defines the distance between two straight lines extending through the vertex M% and in addition the blood south degree vector h ° parallel. Similarly, the thickness vector β is shown to extend through the vertex V # V2 and at a distance from the height vector \ cut. < ^ Parameter t based on the parameters shown in Figure 3. Calculate thickness according to the following calculation instructions 88012 -14- 200404266 ^ _ ^ $ 0¾ h. = 〇 \ F / hj Otherwise ′ = 0 if A. 4 = 0 l ^ / maxG. ，、） Otherwise ㈣ 本 发 @ 之 — preferably with the index rotation too Α Η 1 depending on the need to calculate the vertex 视 universal d, you can then calculate the direction of rotation. This is used to calculate the rotation direction d and area A from the properties of,, and 彖: The difference between ㈣ and d = sign (hz) A = F / 2 where: The area across the parallelogram of hG and \. The direction d has a numerical value of clockwise rotation +1 and a numerical value of counterclockwise rotation. In the case, the trajectory degenerates into a point or a line, and in this case, the rotation direction d is 0. After the thickness parameter t is determined, and if necessary, the rotation direction d and the area a are determined, and then the clamping dimension c is calculated. The clamping dimension 0 is a linear function of the process across the thickness parameter 1. The process is positioned at a settable performance parameter p and table.
/、/ 戈人 ^ m a X 所定義之所得邊緣之最大長度之間。若t=p，則夾緊尺寸c 具有一P值，所得軌跡之最大面積A*係為此設定而設定，其 中：A* =P2。在設定參數c的基礎上，依據下面的計算說明 進行決定初始夾緊尺寸。 〇<P<C<Eaax/, / Geren ^ m a X Defined between the maximum length of the resulting edge. If t = p, the clamping dimension c has a value of P, and the maximum area A * of the obtained trajectory is set for this setting, where: A * = P2. After setting parameter c, determine the initial clamping size according to the following calculation instructions. 〇 < P < C < Eaax
c〇*max(Pfc) 88012 -15- 200404266 在圖4中標繪與厚度參數t相對之夾緊尺寸〇之進程，且如 所見’ 時夾緊參數值係c=Emax且從此值開始以線性方式 向下減少至P值’其在t=p時達到。到此值為止，夾緊參數c-之數值在P值保持不變。圖4之最下面的曲線顯示初始邊界. 值及/或初始夾緊尺寸％及/或相對於厚度參數t之進程。圖4 中，取下面的曲線說明mipmap位準為〇時夾緊框％之最先計 算尺寸。此處顯示所採用解析度之測量。曲線定性地說明 以下特性：具有較小的t，即具有如此一較小區域之較窄軌 跡，夾緊尺寸且因而紋理之較佳解析度增加，且該紋理之 texel尺寸與軌跡之尺寸成比例減小。由引起之方向向 上之夾緊確保最大可接納邊緣長度，由p引起之方向向下之 爽緊限制處理之持料間。p值越大，向較低解析度之跳躍 進行得越晚，從而引起軌跡之區域增加。上面的曲線e， 應於mipmap位準m之座標變換％。若爪不等於'q,則需m要 後者，且因而需要縮小。 以下將參考圖5詳細說明如何計算必要的位準爪叫 及所需要的軌跡尺寸之縮小。 q 最初要假定對於所呈現之軌跡，在軌跡之初始尺度及形 狀中存在-mipmap位$ ’該吻卿位準避免縮小軌跡。藉 由此最小mipmap位準確保軌跡之邊界框之側面都不大於以 上述方式決疋的夾緊尺寸c〇。除了軌跡2〇〇，圖5亦示範性 顯示邊界框202,且依據τ面的計算說明得出邊界框2〇2及 所需要的mipmap位準mreq : 88012 -16- 200404266 ^Βίη δ =〔max (v0rX，vlrX, %x，v3rX)、 咖 1 顏 <v0,y，Vl,y，ν〜，v3,y)> δ 二 δ 繼 mzeq^max(0r ceil {log2 'max (bx/ bv)' co ) 其中「上限（ceil)」函數說明，括號中的項朝方向+0〇增加至 下一整數值。圖5顯示上述計算說明中得出的參數bmin及b， 且亦可在計算說明中得出之參數bmax係從座標系統原點延伸 至向量b之頂點之向量（但為了清楚起見沒有顯示）。 _ 為了獲得欲應用之mipmap位準m，依據下面的計算說明 夾緊所需要的mipmap位準至最高可用位準值μ : ,_EL max m=min(Mmax?mreq) 然而若發現需要的以丨口㈤叩位準m係小於由邊界框所指定 的mipmap位準，即係小於，必須減小軌跡之尺寸，使 邊軌跡適合夾緊框。在mipmap校正夾緊尺寸、的基礎上計 算夾緊框，其依據下面的計算說明決定： cm=rnax(P.2m，c + (2m-l).Emax) · 在圖4中亦標繪已校正之夾緊尺寸cm參數之進程。 圖5顯示在已校正之夾緊尺寸、的基礎上產生的夾緊框 2〇4。將軌跡200之尺寸減小至已縮小軌跡2〇6，使得最初軌 跡之頂點vG至、以一方式（轉換後的頂點係配置於夾緊框1 勺k、彖上）轉換成頂點ν。’至〜’。依據下面的計算說明引起 最初頂點轉換成修正後的頂點： 88012 200404266 fxry*mini1,, V Cm . V, ΓΛ〇1 S. ¢:)) 其中： fx、與y方向的縮放因數。 在最後一區塊中，減小後的軌，、 • 、V i的座標必須變換至 nnpmap位準m，其依據下面的計算說明進行： K 88 2"ra . ψχ ::卜’本發.方法規定根據厚度參數t提供放大位準，其 後用於放大具有次_尺寸之軌跡以避免在呈現包括 稷數個軌跡（軌跡中之時間與空間的人工因素。 一旦由於軌跡尺寸之減小改變厚 、 、 、 又7予度參數t，斫必須設足厚 度參數。由於厚度參數t传一夂 你各向芳性特性，其可藉由在上 述計算說明的基礎上彦 產生3、、値小頂點向量的一新的厚度參 數來計算’然而此法涉及卓 田 、 、 乂夂敉大數1的計算費用。然而依據 車乂佳/、缸員她例藉由採用定向縮放因數t與可以相當少 勺費用近似决疋厚度參數t(方法Q，因而可用下面的方法決 定設定厚度參數Γ : ⑴ t，«) ⑵ t，=t · ^+ fy 2 (3) minify, fyj 如上所述，（2)中所說明之方法較佳。 由可設定之放大參數τ控制放大位準r，其說明一最小厚 度而沒有放大。依據下面的計算說明產生放大位準： 88012 -18· 200404266 T值越高，引入欲呈現之影像的斑點越多，但是同時發現 較少的人工因素。已證明τ為數值心時係有利的。若選擇 Τ=0，則停用任何放大。 與上述決定可改變厚度參數t，類似，有三種可能的方式（方 法r)用於將延遲位4 r轉挺成所選取mipmap位準m ;明確地 說： 1) ·2一a 2) rK=rr 3) r·*ι：，+ -2加1>)·f 稱作1)的方法保持所有mipmap位準的有效過濾尺寸。然 而補償具有小於texe：[之尺寸之元素僅應用於mipmap位準〇 且mipmap位準越鬲，補償效果越差。方法3)確保所有位準 之T的一致性。然而有效過濾尺寸在兩位準之間經受不連: 的擴大JL ’此外’計算係更昂貴。較佳方法2)最終係^與^) 芡間的一折衷且因而理所當然係最容易實施的方法。 藉由上面方式所說明之參數可在隨後的處理步驟中計算 軌跡的顏多。A匕 、 '、目的，提供圖形單元之另一處理級所決 疋的參數，該圖形單元接著以一傳統方式產生軌跡的顏色。 ^逑車父佳具體實施例中，儘管已在具有四個側面的軌 跡的基礎上說明士 " 本發明，但是原則上本發明方法可延伸至 任何執跡。 【圖式簡單說明】 上文已參考附同二、， 1订圖評細說明本發明之較佳具體實施例，其 88012 -19- 200404266 中·· 圖1A與B顯示概述依據本發明之一較佳具體實施例之方 法之一流程圖； 圖2係代表一紋理空間中之示範性軌跡之頂點與邊緣向 量； 圖3係代表該執跡及與該執跡有關的厚度參數； 圖4根據軌跡之厚度說明夾緊尺寸之進程；及 圖5說明軌跡縮小之範例。 【圖式代表符號說明】 100、 102 、104 、106、 108、 110 、112 區 塊 116、 120 、122 、124、 126、 128 、130 區 塊 132、 134、 136、 S136、 138、 140 ^ 142 區 塊 144、 146 、148 、150、 152、 154 、156 區 塊 158、 160 、162 區 塊 104 夾 緊 框 114 指 定 118 決定 136 處 理 級 164 區 段 200 軌跡 88012 •20- 200404266 202 邊界框 204 夾緊框 206 縮小軌跡 88012 -21-c〇 * max (Pfc) 88012 -15- 200404266 In Fig. 4 plot the progress of the clamping dimension 0 relative to the thickness parameter t, and as you can see ', the clamping parameter value is c = Emax and from this value in a linear manner Decrease down to P-value 'which is reached at t = p. Up to this value, the value of the clamping parameter c- remains unchanged at the P value. The bottom curve of FIG. 4 shows the initial boundary value and / or the initial clamping dimension% and / or the progress with respect to the thickness parameter t. In Figure 4, the following curve is taken to illustrate the first calculated size of the clamping frame% when the mipmap level is 0. The measurement of the resolution used is shown here. The curve qualitatively illustrates the following characteristics: with smaller t, that is, a narrower trajectory with such a smaller area, the clamping size and thus the better resolution of the texture is increased, and the texel size of the texture is proportional to the size of the trajectory Decrease. The upward clamping by the induced direction ensures the maximum acceptable edge length, and the tight downward direction caused by the p limits the handling holding room. The larger the p value, the later the jump to the lower resolution is performed, which causes the area of the trajectory to increase. The above curve e should be transformed% at the coordinates of the mipmap level m. If the claw is not equal to 'q, then m is required for the latter, and therefore needs to be reduced. The following will describe in detail how to calculate the necessary level claws and the reduction of the required track size with reference to FIG. 5. q Initially assume that for the presented trajectory, -mipmap bit $ 'exists in the initial scale and shape of the trajectory to avoid shrinking the trajectory. By this minimum mipmap level, it is ensured that the sides of the bounding box of the trajectory are not larger than the clamping dimension c0 determined in the above manner. In addition to the trajectory 200, FIG. 5 also shows the bounding box 202 as an example, and the bounding box 202 and the required mipmap level mreq are obtained according to the calculation description of the τ plane: 88012 -16- 200404266 ^ Βίη δ = [max (v0rX, vlrX,% x, v3rX), coffee 1 < v0, y, Vl, y, ν ~, v3, y) > δ two δ Following mzeq ^ max (0r ceil {log2 'max (bx / bv) 'co) Where the "ceil" function indicates that the terms in parentheses increase in the direction + 0〇 to the next integer value. Figure 5 shows the parameters bmin and b obtained in the above calculation description, and the parameter bmax, which can also be obtained in the calculation description, is a vector extending from the origin of the coordinate system to the vertex of the vector b (but not shown for clarity) . _ In order to obtain the mipmap level m to be applied, according to the following calculations, the mipmap level required for clamping is to the highest available level value μ:, _EL max m = min (Mmax? Mreq) However, if it is found that The mouth level m is less than the mipmap level specified by the bounding box, that is, it is less than, the size of the trajectory must be reduced to make the edge trajectory suitable for the clamping frame. The clamping frame is calculated on the basis of mipmap's correction of the clamping dimensions. It is determined according to the following calculation instructions: cm = rnax (P.2m, c + (2m-l) .Emax) · It is also plotted in Figure 4 The process of correction of the clamping dimension cm parameter. Fig. 5 shows the clamping frame 204 generated based on the corrected clamping dimensions. The size of the trajectory 200 is reduced to the reduced trajectory 206, so that the vertices vG of the original trajectory are converted into vertices ν in a manner (the converted vertices are arranged on the scoop k, 彖 of the clamping frame 1). 'to~'. According to the following calculation instructions, the initial vertices are converted into modified vertices: 88012 200404266 fxry * mini1 ,, V Cm. V, ΓΛ〇1 S. ¢ :)) where: fx, the scaling factor in the y direction. In the last block, the coordinates of the reduced orbit must be transformed to the nnpmap level m according to the following calculation instructions: K 88 2 " ra. Ψχ :: 卜 '本 发. The method provides that the magnification level is provided according to the thickness parameter t, which is then used to enlarge the trajectory with sub_size to avoid the artificial factors including time and space in the presentation of several trajectories (time and space in the trajectory. Once changed due to the reduction of the trajectory size Thick,,, and 7 predetermine the parameter t, and 斫 must be set to a sufficient thickness parameter. Since the thickness parameter t is passed on to your isotropic aromatic properties, it can be generated by using the above calculation and explanation. A new thickness parameter of the vertex vector is used to calculate 'However, this method involves the calculation cost of Zhuo Tian, 乂 夂 敉, and large number 1. However, according to Che Yanjia /, the crew member can use the directional scaling factor t and can be equivalent The cost of the spoon is approximately determined by the thickness parameter t (method Q, so the following method can be used to determine the set thickness parameter Γ: ⑴ t, «) ⑵ t, = t · ^ + fy 2 (3) minify, fyj as described above, ( The method described in 2) is better. The set magnification parameter τ controls the magnification level r, which indicates a minimum thickness without magnification. The magnification level is generated according to the following calculation instructions: 88012 -18 · 200404266 The higher the value of T, the more speckles are introduced into the image to be presented, However, fewer artificial factors were found at the same time. It has been shown that τ is advantageous when the numerical center is selected. If T = 0 is selected, any amplification is disabled. Similar to the above decision, the thickness parameter t can be changed. There are three possible ways (methods) r) is used to turn the delay bit 4 r to the selected mipmap level m; specifically: 1) 2-a 2) rK = rr 3) r · * ι :, + -2 plus 1 >) · The method called f) maintains the effective filtering size at all mipmap levels. However, the compensation has a size smaller than texe: [only applies to mipmap level 0, and the higher the mipmap level, the worse the compensation effect. Method 3) Ensure the consistency of T across all levels. However, the effective filtering size is not connected between two digits: the expanded JL is more expensive. The preferred method 2) is ultimately a compromise between ^ and ^) 芡 and is therefore the easiest to implement. With the parameters described above, the trajectory can be calculated in the subsequent processing steps. A,, and purpose provide parameters determined by another processing level of the graphics unit, which then generates the color of the track in a conventional manner. ^ In the specific embodiment of Che Fujia, although the present invention has been described on the basis of a track with four sides, the method of the present invention can be extended to any track in principle. [Brief Description of the Drawings] The preferred embodiment of the present invention has been described in detail with reference to the attached drawings 2 and 1 above. The figure shows 88012 -19- 200404266. Figure 1A and B show an overview according to one of the present invention. A flowchart of a method of a preferred embodiment; Figure 2 represents the vertices and edge vectors of an exemplary trajectory in a texture space; Figure 3 represents the track and the thickness parameters related to the track; Figure 4 is based on The thickness of the trajectory illustrates the progress of the clamping dimension; and FIG. 5 illustrates an example of the trajectory reduction. [Schematic representation of symbols] 100, 102, 104, 106, 108, 110, 112 blocks 116, 120, 122, 124, 126, 128, 130 blocks 132, 134, 136, S136, 138, 140 ^ 142 Block 144, 146, 148, 150, 152, 154, 156 Block 158, 160, 162 Block 104 Clamping box 114 Designation 118 Decision 136 Processing level 164 Section 200 Track 88012 • 20- 200404266 202 Bounding box 204 folder Tight box 206 Shrink trajectory 88012 -21-